2x(x-6)-180=0

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Solution for 2x(x-6)-180=0 equation: 


Simplifying
2x(x + -6) + -180 = 0

Reorder the terms:
2x(-6 + x) + -180 = 0
(-6 * 2x + x * 2x) + -180 = 0
(-12x + 2x2) + -180 = 0

Reorder the terms:
-180 + -12x + 2x2 = 0

Solving
-180 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + -6x + x2 = 0

Solving
-90 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -6x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -6x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -6x + x2 = 0 + 90
-6x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-6x + x2 = 90

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 90 + 9

Reorder the terms:
9 + -6x + x2 = 90 + 9

Combine like terms: 90 + 9 = 99
9 + -6x + x2 = 99

Factor a perfect square on the left side:
(x + -3)(x + -3) = 99

Calculate the square root of the right side: 9.949874371

Break this problem into two subproblems by setting 
(x + -3) equal to 9.949874371 and -9.949874371.


Subproblem 1
x + -3 = 9.949874371

Simplifying
x + -3 = 9.949874371

Reorder the terms:
-3 + x = 9.949874371

Solving
-3 + x = 9.949874371

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = 9.949874371 + 3

Combine like terms: -3 + 3 = 0
0 + x = 9.949874371 + 3
x = 9.949874371 + 3

Combine like terms: 9.949874371 + 3 = 12.949874371
x = 12.949874371

Simplifying
x = 12.949874371


Subproblem 2
x + -3 = -9.949874371

Simplifying
x + -3 = -9.949874371

Reorder the terms:
-3 + x = -9.949874371

Solving
-3 + x = -9.949874371

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = -9.949874371 + 3

Combine like terms: -3 + 3 = 0
0 + x = -9.949874371 + 3
x = -9.949874371 + 3

Combine like terms: -9.949874371 + 3 = -6.949874371
x = -6.949874371

Simplifying
x = -6.949874371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.949874371, -6.949874371}
Solution
x = {12.949874371, -6.949874371}

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